SPH Accuracy to Describe the Wave Impact on a Tall Structure (benchmark case 1)

SPH Accuracy to Describe the Wave Impact on a Tall Structure (benchmark case 1) M. GómezG mez-gesteira 1, A. J. C. Crespo 1, M. decastro 1 & R. A. Dalrymple 2 1 GRUPO DE FÍSICA DE LA ATMÓSFERA Y DEL OCÉANO, UNIVERSIDADE DE VIGO 2 DEPARTMENT of CIVIL ENGINEERING, JOHNS HOPKINS UNIVERSITY

A bitofhistory 2002 Tony & I created our SPH3D We needed an experimental case to check the model We found a suitable case at engr.smu.edu/waves/project.html (P. Raad)

Experimental setup Forces exerted on structure were measured. Velocity at a single point near the bottom was measured Yeh and Petroff experimental setup: side view and top view

Initial SPH configuration: : fluid and boundary particles MODEL PARAMETERS 3D cubic spline kernel XSPH correction with ε =0.5 INITIAL AND BOUNDARY CONDITIONS Fluid particles: initial velocity = 0 ρ 0 = 1000 kg m -3

WITH WET BED WAVE DUE to the INITIALLY WET BED

Experimental limitations The velocity series starts when the wave arrives at the control point There was not information about gate movement Data: Gaps and overlap The amount of water near bed was not accurately determined

Comparison between numerical (solid line) and experimental data (dots). Velocity (m s 1 ) 3 2 1 0 1 0 0.5 1 1.5 2 2.5 Time (s) 40 Force (N) 20 0 20 0.5 1 1.5 2 2.5 Time (s)

SPH DESCRIPTION: Compiling Options KERNEL 2D Cubic Spline OR 3D Quadratic Liu (2003) Tensile Instability Correction (when needed) Monaghan (2000) Kernel Normalization Bonet and Kulasegaram (2000) Momentum equation Monaghan (1992) Shepard Shepard filter (1968)

SPH DESCRIPTION: Compiling Options Differential Equation for Density Monaghan (1992) Equation of state Batchelor (1974) XSPH Variant Monaghan (1989) Boundary Conditions Repulsive Force (Monaghan & Koss 1999) Dynamic Boundaries (Dalrymple & Knio 2001) Time Algorithm Verlet (1967) Predictor- Corrector (Monaghan 1992) Variable Time Step Monaghan (1992)

SPH DESCRIPTION: Compiling Options VISCOSITY Artificial Viscosity Monaghan (1992) Laminar Viscosity Gotoh et al. (2004) Sub-Particle Scale Turbulence Initial Conditions Gotoh et al. (2004) Square Cells (Monaghan & Koss 1999) Staggered Grid (Gómez- Gesteira & Dalrymple 2004)

Statistical protocol Partition of equally spaced data (velocity & force) 1 second 100 points (dt=0.01 s) Signal amplitude A i= 1 = 100 100 num ( Vali ) exp ( Vali ) i= 1 2 2 A 1 Signal Phase 100 num exp ( Vali Vali ) i= 1 P = 100 P 0 2 exp ( Vali ) i= 1 2

Artificial Viscosity (Velocity) Velocity P A 0.25 1.02 1 0.98 0.2 0.96 0.15 0.94 0.92 0.1 0.9 0.88 0.05 0.86 0.84 0.82 0 0.015 0.015 0.02 0.02 0.025 0.025 0.03 0.03 0.035 0.035 h

Artificial Viscosity (Force) Force P A 1.2 1 0.8 0.6 0.4 0.2 0 0.015 0.02 0.025 0.03 0.035 h h

SPS (Velocity) Velocity P A 1.05 0.3 0.251 0.2 0.95 0.15 0.9 0.1 0.05 0.85 0.8 0 0.015 0.02 0.025 0.03 0.035 h

SPS (Force) Force P A 1.4 1.6 1.2 1.4 1.2 1 1 0.8 0.6 0.8 0.6 0.4 0.2 0 0.015 0.02 0.025 0.03 0.035 h

The price of improvement??? 140000 120000 Number of Particles 100000 80000 60000 40000 20000 N h 3 0 0.015 0.02 0.025 0.03 0.035 h

The price of improvement??? 16 14 12 RUN(hours) 10 8 6 RUN N 2 4 2 0 20000 70000 120000 Num ber of Particles

The price of improvement??? 16 14 12 RUN (hours) 10 8 6 4 RUN h 5 2 0 0.015 0.02 0.025 0.03 0.035 h

Thanks!!!

WITH WET BED WAVE DUE to the INITIALLY WET BED

INITIAL CONDITIONS PARTICLES WERE PLACED ON FIXED POSITIONS AND ZERO INITIAL VELOCITY FLUID PARTICLES BCC LATTICE BOUNDARY CONDITIONS Dalrymple & Knio (2001) AVOID WALL PENETRATION BOUNDARY PARTICLES DO NOT MOVE B.P.. FOLLOW Continuity Equation Equation of State

BOUNDARY CONDITIONS Density and pressure increase when a fluid particle approaches the boundary. 2h fluid particle b V b < 0 boundary particle a V a = 0 2h P a increases boundary particle repulses fluid particle

Initial SPH configuration: : fluid and boundary particles MODEL PARAMETERS 3D cubic spline kernel h = 0.0331 m XSPH correction with ε =0.5 INTIAL AND BOUNDARY CONDITIONS Fluid particles: dx=dy dy=dz=0.025 m initial velocity = 0 ρ 0 = 1000 kg m -3

Patong Beach. Runup ramped into second floor

MITIGATION Gate Structure Back Wall 0.35 Seawall Slope 0.6 d 0 was kept constant in this way the conditioning wave was the same in all simulations. Z X 0. 4 0.13 d 0 =0.3 5 d=0.3 0.1 5 0.3 Two free parameters will be considered: d and slope. 0.7 Y 2 =0.45 Y 1 =0.25 d: : different distances from seawall to structure. (d = 0.25 0.3 0.35 m) Y X Other parameters in tsunami mitigation ( like barrier height and d) were studied in Crespo et al. 2005

d: : different distances from seawall to structure. d = 0.25 m

d: : different distances from seawall to structure. d = 0.30 m

d: : different distances from seawall to structure. d = 0.35 m

MITIGATION Gate Structure Back Wall 0.35 Seawall Slope 0.6 d 0 was kept constant in this way the conditioning wave was the same in all simulations. Z X 0. 4 0.13 d 0 =0.3 5 d=0.3 0.1 5 0.3 Two free parameters will be considered: d and slope. 0.7 Y 2 =0.45 Y 1 =0.25 d: : different distances from seawall to structure. (d = 0.25 0.3 0.35 m) Y X slope: : landward or seaward (0º, 5º, 10º, 15º, 20º)

Seaward

Landward

Landward Seaward

Highest Impact Points 25cm 30cm 35cm 0.6 0.5 0.4 H structure 0.3 0.2 0.1 0-25 -20-15 -10-5 0 5 10 15 20 25 slope (grades) Seaward Landward

Maximum Moment 25cm 30cm 35cm 2.5 2 Mn 1.5 1 0.5 0-25 -20-15 -10-5 0 5 10 15 20 25 slope (grades) Seaward Landward

The best situation will be Seaward

Correlated with damage_scour

MITIGATION d 0 was kept constant in this way the conditioning wave was the same in all simulations. Velocity along lateral extent was measured at different transects in X.

A : without seawall B : continuous seawall C : open seawall

C : open seawall

TRANSECT 1 X = 0.95 m A B C v (m/s) 4.5 4 3.5 3 2.5 2 1.5 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 y (m) TRANSECT 4 X = 1.25 m A B C v (m/s) 4.5 4 3.5 3 2.5 2 1.5 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 y (m) A : without seawall B : continuous seawall C : open seawall

TRANSECT 1 X = 0.95 m A B C 4.5 4 3.5 3 2.5 2 1.5 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 y (m) A : without seawall B : seawall closing C : seawall opening

TRANSECT 4 X = 1.25 m A B C 4.5 4 3.5 v (m/s) 3 2.5 2 1.5 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 y (m) A : without seawall B : seawall closing C : seawall opening

In general, dam velocity with a open seawall is higher in the opening

A solution would be

CONCLUDING REMARKS The 3D version of the SPH model has proven to be a suitable tool to reproduce phenomena related to wave collision with a structure. In particular, the presence of seawalls to mitigate the effect of o large waves on coastal structures was considered. Key parameters to control the mitigation process: - same wave condition - dam break water release - d distance from the seawall to the structure - seawall slope - seawall opening

CONCLUDING REMARKS SEAWALL SLOPE Impact points are higher with landward seawall slope. And they are lower with seaward seawall slope. In the same way, moment is higher with landward seawall slope and it is lower with seaward slope. So a landward seawall is more dangerous and the best situation to mitigate tsunami waves is a seaward seawall.

CONCLUDING REMARKS SEAWALL OPENING In general, velocity measured without seawall is constant along lateral extent. Velocity measured with a continuous seawall to mitigate waves is lower than in the case without seawall. And velocity measured in the lateral extents corresponding to opening of the seawall is the highest. So is the most dangerous situation of them. A A solution would be build a seawall of the same lateral extent than the opening and place it before the opened seawall.

THANK YOU VERY MUCH MOITO OBRIGADO